This page contains exploratory analysis for the trawl data from JSOES.

Top ten taxa by mean density.
species mean_n_per_km sd_n_per_km
sea_nettle 44.5 268.7
water_jelly 41.6 243.8
california_market_squid 15.3 91.8
coho_salmon_yearling 2.4 5.6
sablefish 2.0 24.8
chum_salmon_juvenile 1.2 5.1
chinook_salmon_subyearling_interior_fa 0.7 2.4
moon_jelly 0.5 9.2
chinook_salmon_subyearling_scg_f 0.4 4.0
chinook_salmon_yearling_interior_fa 0.3 0.8
Top ten taxa by frequency of occurrence.
species n prop_samples
coho_salmon_yearling 712 0.55
water_jelly 707 0.55
california_market_squid 491 0.38
sea_nettle 486 0.38
chinook_salmon_yearling_interior_fa 432 0.33
chum_salmon_juvenile 393 0.30
chinook_salmon_yearling_interior_sp 321 0.25
chinook_salmon_mixed_age_juvenile 319 0.25
chinook_salmon_subyearling_interior_fa 312 0.24
wolf_eel 231 0.18

Plotting distributions of some common taxa

Some focal taxa: - Coho salmon yearlings - Interior Columbia Fall Chinook salmon yearlings - Interior Columbia Spring Chinook salmon yearlings - Water jellies (highest density taxon)

By taking the mean log density across the survey region, we can also create a crude index of abundance.


From the maps and the indices of abundance, we see that the most pronounced trend is in Water Jellies, with what appears to be a regime shift from a period of relatively lower abundance before the Blob (1999-2013) to much higher abundances during and after the Blob (2014-2023).

Temporal and Spatial Autocorrelation

Before fitting any spatiotemporal models, we must explore the spatial and temporal autocorrelation in the data.

Temporal structure

We can first inspect the autocorrelation in our Calanus marshallae and Calanus pacificus mean annual time series.

None of the four taxa investigated here show temporal autocorrelation.

We can also inspect temporal autocorrelation at the scale of individual stations. To reduce the number of individual ACF plots, I have instead plotted histograms showing the distribution of lag 1 autocorrelation across station for each of our two four test species, along with time series plots for the stations that had significant autocorrelation at this lag:

Despite the lack of temporal autocorrelation at the coastwide scale, for each taxon there are a number of stations that show temporal autocorrelation.

Spatial structure

To investigate spatial autocorrelation, we will calculate two metrics: Semivariance and Moran’s I. Semivariance, visualized using a semivariogram, allows us to examine how spatial autocorrelation decays with increasing distance. In a semivariogram, high spatial autocorrelation appears as as a clear slope that then reaches a plateau at the distance at which there is no spatial autocorrelation, as seen in this image from Wikipedia:

An example Variogram.
An example Variogram.

To calculate the semivariance, we compute the variance of the difference between values (in our case, the log density) for different distances between samples. It is given by the following formula:

\[ \gamma(h) = \frac{1}{2} \mathrm{Var}( \log(x_i) - \log(x_{i+h}) ) \] Where \(h\) is the distance between two points, \(x_i\) is the value of the log density at one location and \(x_{i+h}\) is value of the log density at a location \(h\) distance away. Multiplying by \(\frac{1}{2}\) accounts for the fact that the formula accounts for the variance arising at both points.

From the semivariance, we can then construct a semivariogram, which depicts the spatial autocorrelation of samples. A semivariogram takes the semivariance calculated for each pair of points and summarizes it by taking the mean value across each bin.

Moran’s I is a measure of the overall clustering of the spatial data and tests if there is support to reject the null hypothesis of no spatial structure.

Given that we did not see much evidence for temporal autocorrelation, we will examine the evidence for spatial autocorrelation on a year by year basis. As such, we will construct a separate semivariogram and calculate Moran’s I separately for each year. To summarize the Moran’s I results, we show the p-value for Moran’s I for each year, with the blue dashed line showing a p-value of 0.05.

We will first examine spatial autocorrelation in Yearling Coho Salmon.



We will first examine spatial autocorrelation in Yearling Interior Spring Chinook Salmon.

We will first examine spatial autocorrelation in Yearling Interior Fall Chinook Salmon.

We will first examine spatial autocorrelation in Water Jellies.

Based on the Moran’s I results, we see that there is evidence for spatial clustering in some years than others. There are also notably more years where the Moran’s I value is significant for these taxa than there are for the two copepod species examined in the JSOES Bongo exploratory analysis. However, there is not a clear slope to the semivariogram, which indicates that the degree of spatial autocorrelation at our sampling variation and that there is a lot of noise in our data. It suggests that all of our taxa are quite patchy, with these patches occurring on a scale less than the scale of the sampling resolution (which is 5 nm along a single transect orthogonal to the coast). This is similar to our results for two copepod species from the JSOES Bongo net data.